Please provide answers

Question

In a demographic study, the population and total income of a certain region were estimated from other data, and both estimates had lower and upper limits. At the time of the estimates, was the per capita income for the region greater than $16,500?
(1) The lower limit for the estimate of the population was 330,000 people.
(2) The lower limit for the estimate of the total income was $5,500,000,000.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Sanket05 · Answer

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?
(1) x is a multiple of 9.
(2) y is a multiple of 25.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

JeffB · Answer

Sanket05 wrote:If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?
(1) x is a multiple of 9.
(2) y is a multiple of 25.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Is the first answer E? If so I'll try to explain

Second one is a little easier for me:

X is a multiple of 6, so it has a 2 & 3
Y is a multiple of 14, so it has a 2 & 7

Is xy a multiple of 105, which has factors:
(21)(5)
(3) (7) & (5)

So we already have a (3) from X and a (7) from Y, so were looking for a 5 to ensure x*y is a multiple of 105.

A: X is a multiple of 9(3 & 3) - We already have a 3 and we are still looking for our 5. No help. Insuff.

B: Y is a multiple of 25(5 & 5) - So now we have our 5.

We now know we have the needed factors. 3,7, and 5.

B is sufficient.

Hopefully that helps.

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